Are the claims made about the http://en.wikipedia.org/wiki/High_beta_fusion_reactor realistic? Can such a small fusion reactor really work?
Nuclear Physics – Can the High Beta Fusion Reactor Work?
fusionnuclear-engineeringnuclear-physicsplasma-physics
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You are referring to scaling laws for the energy confinement time ($\tau_{E}$), which is a key performance parameter for a fusion reactor. For example, a stellarator currently has \begin{equation} \tau_{E} \propto \, a^{2.33} B^{0.85}, \end{equation} where $a$ is the minor radius and $B$ is the toroidal magnetic field. This particular scaling is of the Bohm type, which is found during low confinement operation. During high confinement operation, an improved scaling of the gyro-Bohm type is present.
To answer your question, I will derive the origin of the above scaling using general principles (see sec. 7.6.4, here). Exponential degradation of confinement is generally assumed, which gives the following confinement time for particles in a cylindrical device with minor radius $a$ and length $L$, \begin{equation} \tau_E \approx \frac{N}{dN/dt}= \frac{n \pi a^2 L}{\Gamma_{\perp} 2 \pi a L} = \frac{n a}{2 \Gamma_{\perp}}\,, \end{equation} where $N$ is the number of ion-electron pairs, $n$ is the number density and $\Gamma_{\perp}$ is the cross-field particle flux with diffusion coefficient D, \begin{equation} \Gamma_{\perp}=- D \,\nabla n\,. %= v_{\perp} n\,. \end{equation} The normalized density gradient scales with the machine size as $\frac{\nabla n}{n} \propto \frac{1}{a}$, giving \begin{equation} \tau_E \propto \frac{a^2}{D}\,. \end{equation} Physically, the particle diffusion in strongly magnetized plasmas is carried by turbulence that is driven by gradients such as the ion temperature gradient or density gradient. This so-called drift wave turbulence can be analytically shown (see Eq. 21.39, here) to have a diffusion coefficient \begin{equation} D\approx \frac{1}{k_{\perp}a}\frac{k_B T_e}{e B}\propto\frac{1}{k_{\perp}a}\frac{T_e}{B} \,, \end{equation} where $k_{\perp}$ is the wavenumber of turbulent fluctuations perpendicular to the magnetic field.
In the worst-case scenario, the fluctuations occur on the scale of the minor radius due to global effects, $k_{\perp}\approx\frac{1}{a}$. This gives the Bohm diffusion, \begin{equation} \tau_E \propto \frac{a^2 B}{T_e}\,. \end{equation}
In the best-case scenario, the fluctuations occur on the ion gyro-radius scale, $k_{\perp}\approx\frac{1}{\rho_i}$, due to micro-turbulence that is much smaller than the machine size, where the ion gyro-radius is given by \begin{equation} \rho_i=\frac{\sqrt{k_B T_i m_i}}{e B}\,. \end{equation} In this case, we get the gyro-Bohm scaling, which is more favorable by factor $\frac{a}{\rho_i}\gtrsim 1000$, \begin{equation} \tau_E \propto \frac{a^2 B}{T_e} \left(\frac{a}{\rho_i}\right)\,. \end{equation} Due to this very favorable scaling with size, ITER is projected to become the first machine to get 10 times more fusion power out than heating power in (with $^2H$+$^3H$), and you probably don't need to make the device several kilometers large for $^1H$+$^{11}B$ fusion.
The example of a Molotov bomb, a favorite of anarchists, and a car engine are a good analogy. The technology needed to contain the energies in a fusion reaction is much harder than the one needed for a car engine because of the MeV energies needed to initiate fusion. Once initiated it is explosive, so it must be engineered into small explosions from which energy can be extracted continuously.
Various ways of controlling fusion in a hot plasma of fusible materials, isotopes of hydrogen mainly, have been proposed and are being worked on. The tokamak is the basis of the international collaboration aiming to build an industrial prototype, ITER..
It is mainly an engineering problem coupled with the sociological problem of so many engineers and scientists working together in a project controlled by many research institutes. ( "too many cooks spoil the broth")
Also just wanted to know if we can continue this fusion reaction to generate precious heavy metals, is it possible?
Heavy metals are on the wrong curve for fusion, which can happen with elements up to iron or so. Each specific reaction will have to be considered, and it will be a completely different problem.
Best Answer
I personally doubt that the Compact Fusion Reactor as presented by Lockheed Martin last week can work, but I haven't seen enough information to be certain. And to some extent, you never know until you try. (As I understand it, they only have a very early prototype, I mean try as in a full scale prototype.)
What I think I can say with certainty, is that it won't be as small as they claim - "can fit on the back of a truck". Trucks are about the same width as standard containers, so about 2.5m wide. I've had to make quite a few guesses, but I've tried to justify them and choose the smallest size possible.
In the second image here, you can see a grey blanket around the device which absorbs 14MeV neutrons to generate tritium and protect the rest of the plant. The internal coils will also need such a blanket to protect them (it's unclear if the orange skin is this blanket, or just the cryostat). It's also unclear if the outer coils are superconducting or not, but I'll assume they are otherwise the ohmic losses use too much of the power you're supposed to be generating. Superconducting coils need to be cooled with liquid helium and insulated inside a cryostat.
Blankets for a tokamak reactor are estimated at 1m thick. I'm not sure if this is dictated by the tritium breeding or the protection. If it's protection, you might be able to reduce their thickness if you're operating at 100MW instead of 1GW, so let's be optimistic and assume 0.2m thick. I'll assume the same width for the coils and the cryostat (probably optimistic again). I'll neglect any structural elements. So going from the outside of the machine to the centre we have
They don't give any figures for the size of the plasma, but I think it just looks silly if the plasma diameter is less than a third of the coil diameter, so I'll put 0.5m in both of those plasma columns. (Note that this is a very small distance between where the fusion happens at 10^8Kelvin and the wall at 10^3K, and would be extremely good magnetic confinement.)
Totalling up gives 2.6m from the outside to the centre, so the machine is about two trucks wide already. You might give them the benefit of the doubt at this stage, even though all those values were optimistic. But then you need to add peripherals:
heating system (the neutral beam injectors shown in the Lockheed diagram are usually about the size of a truck by themselves)
cryogenic plant for liquid helium (at least half a truck)
power supplies for the coils
vacuum pumping system
steam turbine
bioshield. Even the 1m blanket on a tokamak doesn't block all of the 14MeV neutrons. Safety regulations will require a few metres of concrete shielding in all directions (multiple trucks)
So even if it would work, I don't think anyone will be putting it on a plane.